Why gigantic numbers baffle the mind

Image credit: Shannon M. Lutman/Getty Images
A SMALL PROBLEM WITH BIG NUMBERS

Our ancient ancestors had no need to understand excessively large numbers as their everyday dealings were with single-digits, such as two fish or three spears. Unlike us, they did not live in a world comprised of millions of streets, billions of people, and trillions of debt. And they certainly never encountered a Rubik’s cube with 43 quintillion possible configurations (that’s 18 zeros)!

In contrast, today’s news broadcasts often report absurdly huge numbers as businesses, scientists, and governments increasingly think in terms of millions (of dollars), billions (of stars), and trillions (in bailouts). These mathematical names are tossed around with casual disregard, thereby sealing their place in common parlance. Still, many of us do not have a visceral grasp of their size.

Understanding giant numbers is far from second nature – they perplex the human mind which is yet to latch on to the modern world’s explosion of massive numbers. As noted by one leading anthropologist, as a species we have evolved capacities that “… are naturally good at discriminating small quantities and naturally poor at discriminating large quantities”.

While getting a solid handle on incredibly big numbers isn’t easy, it’s not a problem for Google founders, Larry Page and Sergey Brin, who both grew up fascinated with mathematics. So, when they registered the name of their new Internet search company in 1997, they chose the mathematical term, googol. Googol is the label for 10 raised to the hundredth power (10100) or 1 followed by 100 zeros.

Our young tech entrepreneurs thought that googol was an appropriate name for their search engine as it was going to index an unfathomable number of Internet web pages. However, due to a typographical error, the name was incorrectly typed as Google; the name stuck and Google Inc. was born.

Big numbers befuddle us – and not because we misspell them. Numbers as large as a googol are hard to comprehend and referring to them by name doesn’t help. There is not a googol of anything in the universe as the number is so mind-bogglingly mammoth it has no practical application.

Of course, smaller numbers used to quantify commonplace things – such as 2 dogs, 25 people, and 1,000 cars – are easy to comprehend. But when we encounter larger numbers, like a quadrillion, it becomes increasingly difficult to conceptualise them. Such numbers are so abstract, our eyes glaze over.

Consider a trillion – it effortlessly rolls off the tongue. Yet, when we express it in exponential format (1012) or its full format (1,000,000,000,000), we start to get a sense of how gargantuan it is. One trillion is a thousand billion, or comparably a million million. Whichever way you look at it, there are too many noughts to make sense of, so let’s put this number into perspective.

If you had spent $1 million a day since the birth of Jesus Christ, you still wouldn’t have chalked up $1 trillion in purchases. If you travelled back in time by a trillion seconds, you would end up circa 30,000 BC. And if you were to spend $1 million an hour, non-stop for 24 hours a day, it would take you 114 years to burn through $1 trillion.

In August, 2018 Apple became the first company in the world to crossover in to the four-comma club when its market capitalisation surpassed $1 trillion. Two years later, Apple’s market value doubled, making it the first publicly traded US company to pass the $2 trillion threshold.

World Bank data reveals that only seven countries have annual GDP figures greater than Apple’s $2 trillion value. With this amount to spend, you could buy Australia and New Zealand and still have a pocket full of change. You could also end world hunger many times over according to the United Nations.

Investopedia calculated that to equal Apple’s $2 trillion market cap, you would have to combine the net worth of the world’s top 24 billionaires. This provides a nice segue to our next humongous number – a billion. Using scientific notation, this number is expressed as 109 – the superscript tells you how many zeros there are after the one.

After discussing a trillion, a billion might sound small – but it’s not. Each billion is equivalent to a thousand million. Could you live on a billion dollars for the rest of your life? Well, spare a thought for the world’s richest individuals who each face the challenge of surviving on personal fortunes of over $100 billion.

In March each year, the American business magazine, Forbes, publishes a list of the wealthiest billionaires in the world. The 2021 Forbes list shows that Amazon founder, Jeff Bezos, is the world’s richest person, with a net worth of $177 billion.

Entrepreneur, Elon Musk, rocketed into number two spot with a $151 billion fortune*. French luxury goods tycoon, Bernard Arnault, took third place with $150 billion under his Louis Vuitton belt. And rounding out the top four in the centibillionaire club is Microsoft co-founder, Bill Gates, whose riches swelled to $124 billion.

The number of billionaires on Forbes 35th annual list exploded to an unprecedented 2,755 people who are collectively worth $13.1 trillion, up from $8 trillion on the 2020 list. Just to provide some perspective to this staggering wealth, Oxfam International reported that prior to the pandemic the (then) 2,153 billionaires in the world had more wealth than the 4.6 billion people who made up 60 per cent of the planet’s population.

If we drop down one notch on our scale of large numbers, we arrive at a more digestible number – a million – which has a power-of-10 notation of 106, where 10 is the base and the 6 is the exponent. A million is a thousand thousand, and while it’s the smallest of the big boys, a million remains the classic benchmark for other massive numbers.

As a million sits at the bottom of the “illions” ladder, it’s easy to view this as a paltry amount, but is that really the case? When was the last time you encountered a million in your daily life? Do you own a million of anything? Have you ever driven a million miles? Do you work in an office with a million employees?

When I was a boy, a millionaire was a very wealthy person whereas today that is considered to be a modest level of wealth. Nevertheless, a million is still a large number and anyone reading this post would be thrilled to strike it rich with a seven-figure windfall. Also, die-hard social media users work overtime trying to rack up a million plus followers.

Humans are visual creatures, so a common strategy for comprehending big numbers is to devise visual representations which provide a sense of scale. You can put a million into perspective by saying that one million acres is the size of 16 million tennis courts. Or that planting one million trees would cover an area of more than 15,000 football fields.

The trick to thinking about large numbers is to relate them to something that is meaningful – even something as simple as seconds. A million seconds takes almost 12 days to elapse, a billion seconds is about 32 years and a trillion seconds equates to around 32,000 years. In a similar vein, you could say that counting to a million would take days, counting to a billion would take years, and counting to a trillion would be impossible in one lifetime.

Telling a child that you could line up 109 Earths across the face of the Sun is far more comprehendible than clinically blurting out that the Sun’s diameter is 1.392 million kms. Equally, reporting that a destructive bushfire has rapidly burned an area equivalent to the size of a football field every second is easier to visualize than saying that millions of acres were destroyed.

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Mathematics is the universal language of humanity and it connects all of us. Around the world and across civilisations, anyone with an elementary education can understand tens, hundreds, and thousands, but many of us struggle to quantify millions, billions, and trillions. So, instead of hurling brain bending numbers at each other, we should break them down so that they make sense for our own experience.

What’s next – getting our minds around a quadrillion (1015)?

*During 2021, Elon Musk passed Jeff Bezos as the richest individual on Earth. According to the Bloomberg Billionaires Index, Musk had a net worth of $220 billion as at 30 January 2022.

Regards

Paul J. Thomas
Chief Executive Officer
Ductus Consulting

Why the future may not need us

Credit: BBC Future
RISE OF SENTIENT ROBOTS

Attempting to predict the future is always a roll of the dice. No one can see around corners, but that has not stopped think-tanks and other forecasters from trying to gaze a few years down the road. Every other week, another report or book is released telling us how tomorrow is going to unfold.

Yet the future has too many variables for anyone to say with certainty what will happen. Long-promised gizmos like flying cars, robot maids and personal jetpacks have failed to materialise for the masses. Similarly, bringing cryogenically frozen corpses back to life remains firmly in the realm of science fiction.

History shows that some innovations turn the world upside down while others flop spectacularly. Determining which discoveries will disrupt the status quo is fraught with danger. This is particularly the case with digital technologies which are taking us into uncharted waters.

I’m not a seer when it comes to the future, nor is Yuval Noah Harari. Professor Harari does not claim to know for certain what’s in store for humanity. Nonetheless, his book – Homo Deus: A Brief History of Tomorrow – provides a provocative and fascinating insight into what might lie ahead.

Harari is a professor of history at the Hebrew University of Jerusalem. His preceding book, the global bestseller – Sapiens: A Brief History of Humankindlaid out the last 70,000 years of human history. It examined how humanity managed to rein in famine, plague and war.

While Sapiens showed us where we have been, Homo Deus points to where we are going. Harari openly admits that predicting the future isn’t as easy as deconstructing the past. Even so, his future orientated sequel provides a glimpse of the forces that will shape the 21st century.

Harari’s central claim is that Homo sapiens (Latin for wise man) will become Homo deus (Latin for god man). We are on the cusp of an evolutionary transition in history that may witness the creation of a new species of superhumans – the man-gods of Harari’s title.

Harari is an atheist, so when he uses the word “god”, he is not referring to a supreme deity who is all-powerful (omnipotent), all-knowing (omniscient) and all-present (omnipresent). Rather, he means humans with life spans greatly extended by science and intelligence vastly enhanced by technology.

Harari believes that humans will increasingly focus on god-like pursuits such as chasing enduring happiness (wellbeing) and everlasting life (wellness). “In seeking bliss and immortality,” he writes, “humans are in fact trying to upgrade themselves into gods”.

Achieving this upgrade will take “divine powers” and will happen through new “techno-humanism” technologies such as genetic modification, artificial intelligence and cyborg engineering. We are approaching a crossroads in evolution where machines will become more human-like and humans will allegedly become more machine-like.

Biology and computing are coming together and could theoretically result in a human brain being directly connected to a computer. That “distant possibility”, says Harari, will be reserved for a tiny number of elites – a superclass of humans – given the significant cost of biotechnology.

There will also be a massive “useless class” who will be pushed to one side by intelligent machines which will do jobs better than people can. The list of occupations where people will be “unemployable” include bus drivers, bartenders, construction labourers, veterinary assistants and telemarketers.

One of the divides between the superclass and useless class will be biological, with the former having superior physical and cognitive capacity and living much longer. A second dividing line between the classes will be artificial intelligence which will give unprecedented power to the few who control the algorithms which run our lives.

To illustrate, at some stage in the future, all vehicles are predicted to be self-driving and one corporation may well control the algorithm that runs the entire transport market. In that scenario, all the economic power previously shared by thousands will be in the hands of a single corporation.

A second example can be found in the operation of the military. Armies – which once consisted of millions of men – are increasingly being dominated by small groups of super-warriors who control technologies like drones and fight cyber wars. The best armies today require a small number of highly professional soldiers using very high-tech equipment.

Across the board, human authority is shifting to algorithms and external data processing systems which, according to Harari, may “know us better than we know ourselves”. Harari envisages that “Dataism” – a universal faith in the power of algorithms – will become sacrosanct.

Our lives will be dominated by non-conscious but highly intelligent algorithms as we are sucked deeper into the online world and turned into faceless data. In this brave new digital world, Dataism will purportedly become our 21st century religion, replacing a homo-centric world with a data-centric world.

Billions of people around the world are regular users of social media and share intimate details of their lives on platforms such as Facebook, YouTube, WhatsApp and Twitter. But all that free browsing and connecting comes at a price – your entire life (which is why I’m not a user, albeit I do utilise Google).

Harari warns that when you get something for free, you are the product. He points out that “in the twenty-first century our personal data is probably the most valuable resource most humans still have to offer, and we are giving it to the tech giants in exchange for email services and funny cat videos”.

The dehumanisation of decision-making is being facilitated by everyday citizens. The algorithms that nowadays make automated decisions – which were formerly the exclusive remit of humans – are being fed a diet of data supplied by us. As noted in an online article by two mathematicians:

An algorithm is a digital recipe: a list of rules for achieving an outcome, using a set of ingredients. Usually, for tech companies, that outcome is to make money by convincing us to buy something or keeping us scrolling in order to show us more advertisements. The ingredients used are the data we provide through our actions online – knowingly or otherwise.

Harari believes that “humankind is poised to replace natural selection with intelligent design, and to extend life from the organic realm into the inorganic”. Still, he is not asserting that the future has to unfold this way. Harari is a great writer and thinker and his book maps the different possibilities that humankind is facing. Nonetheless, he states that our species:

… is likely to upgrade itself step by step, merging with robots and computers in the process, until our descendants will look back and realise that they are no longer the kind of animal that wrote the Bible, built the Great Wall of China and laughed at Charlie Chaplin’s antics.

Frankly, I find Harari’s predictions chilling and hope that they do not come to pass. I don’t want my great-grandchildren to be bio-engineered. I don’t want humans to be turned into flesh and silicon cyborgs. And I don’t want the techno super-rich to live forever by implanting their brains into robots.

My attitude to immortality was outlined in a recent post, The quest for healthy aging and longevity. Assuming I’m right and immortality is never achieved, the unequal availability of life extending procedures will nonetheless take a toll on society. For Harari this means that:

… we might see the emergence of the most unequal societies that ever existed … economic inequality will be translated into biological inequality.

I hope that the world is not spinning too fast to avoid this grim future.

Before you go…

Last year, I read a book by Roger McNamee called Zucked: Waking Up to the Facebook Catastrophe. McNamee was an early mentor to Mark Zuckerberg and a Facebook investor. Nowadays, he spends his time warning people of the dangers of social media platforms. In an article he wrote, McNamee warns that it’s time to wake up to the dark side of Internet technology if we are to avoid a dystopian nightmare. Well worth a read.

One last thing…

I have long believed that the discourse in the mainstream media about artificial intelligence (AI) is grossly exaggerated. This misrepresentation is reinforced by Hollywood which continues to feed the paranoia about AI with a diet of movies portraying robots as evil machines. Filmmakers, along with the media, know that people are predisposed to fear what they do not understand. I do not believe that robots will become human facsimiles and this article does a good job in explaining why our fears of AI are overblown. Also, well worth a read.

Regards

Paul J. Thomas
Chief Executive Officer
Ductus Consulting

The quest for healthy aging and longevity

Credit: World Science Festival
NEVER SAY DIE

The human species has a natural shelf life due to aging – a debilitating condition that no one can escape. Our biological functions decay over time and the Grim Reaper eventually catches up with all of us. Despite the amazing advances in medicine and the resultant rise in life expectancy, you can’t keep Father Time at bay forever. Still, there are those who believe that humans can significantly extend their expiry date.

It is generally accepted that the apparent limit to human lifespan is about 120 years. The life extending treatments necessary to ward off the ailments that accompany old age and stop people living well beyond 120 years do not currently exist. So, at this stage, we are all doomed to age and die – assuming that some other fatal event does not take us out first.

That said, the good news for those who want to stay young and live longer is that scientists are working to recalibrate the human body clock. It’s already evident that people over 50 aren’t aging as fast or poorly as their parents, and anti-aging research is set to improve this trend. Over time, medical treatments to head off the slow march towards death will become increasingly common.

We know that the duration of human life is influenced by genetics, the environment and lifestyle. Yet the causes of aging are extremely complex and unclear. With the rise in longevity clinical trials, more answers – and questions – are emerging. Scientists are now asking whether our natural genetic makeup is limited to a maximum span of 120 years or whether this boundary can be breached.

The study of longevity is a developing science. Our genes harbor many secrets to a long and healthy life and researchers are trying to find the key within our genome to edit out bad stuff. Genes are akin to little packets of information found in each cell in our body. These packets contain critical instructions which tell our body how to grow and develop.

An online article by Nature Publishing Group explains that:

The action of a single gene can have huge effects on how long a creature lives. This may seem hard to believe because so many things go into determining lifespan, including a host of lifestyle factors and a long list of diseases. Nonetheless, remarkable effects on lifespan are seen when particular genes are deleted from an animal’s genetic sequence. Furthermore, research – particularly that involving microscopic roundworms – continues to provide scientists with tantalizing clues about the molecular pathways involved in aging.

Researchers at the University of Rochester have discovered that one of the keys to longevity resides in a gene called Sirtuin 6 or SIRT6. The Sirtuin family of genes and their proteins play a role in controlling aging by repairing damaged DNA, thereby preserving health and youthfulness. SIRT6 has also been identified as a critical regulator of telomere integrity.

Telomeres are an essential part of human cells that affect how our cells age. Telomeres are caps at the end of each strand of DNA which protect our chromosomes, just like the plastic coating (tips) on the ends of shoelaces. Without tips, shoelaces would become frayed and no longer able to do their job. In the same way, without telomeres, DNA strands become damaged resulting in the inability of cells to fully replicate.

The cells in your body are continually dividing and renewing. With each round of cell division, telomeres become shorter. Eventually, our telomeres become so short that the genes they protect could be damaged, so the cells stop dividing and self-destruct. This programmed cell death (called apoptosis) contributes to aging.

Apoptosis is “cell suicide” and scientists believe that reducing the rate of telomere shortening could slow the body’s cellular clock. Research shows that longer telomeres are associated with a longer lifespan while shorter telomeres are connected with the ailments of aging: heart disease, cancer and osteoporosis. If scientists can preserve or elongate telomeres, humanity will be one step closer to a genetic Fountain of Youth.

While most scientists are purely trying to extend life, some researchers are brazenly focussed on helping people dodge death altogether, by turning science fiction into science fact. To many, the quest for immortality seems nonsensical. Even so, Ray Kurzweil, Google’s Director of Engineering, preaches that “immortality is within our grasp”.

Google co-founder, Larry Page, has invested $1.5 billion of Google’s money into a R&D project called Calico, which aims to “cure death”. Calico is short for the California Life Company and the mission of this Google-backed biotech firm is to “harness advanced technologies to increase our understanding of the biology that controls lifespan”. For the masters of the universe at Google, death is the ultimate engineering problem to be solved. The company believes that it will eventually be successful at hacking the code of life.

Aging and death are existential certainties, which is why many consider Google’s anti-death project to be unbridled hubris. While the search for immortality is an epic goal, few believe that Google will solve “the problem” of death. A more likely outcome is that Calico will find ways to dramatically extend human life. That, in itself, raises a series of socio-economic questions regarding overpopulation, class divisions and the affordability of anti-aging technologies.

What seems forgotten by Calico’s backers in their conquest of death is that mortality has value, which is why immortality is not an easy sell. Research reveals that most people don’t like the idea of living forever. As outlined in a 2017 Smithsonian Magazine article:

… a large percentage of today’s population also subscribes to religious beliefs in which the afterlife is something to be welcomed. When the Pew Research Center asked Americans in 2013 whether they would use technologies that allowed them to live to 120 or beyond, 56 percent said no. Two-thirds of respondents believed that radically longer lifespans would strain natural resources, and that these treatments would only ever be available to the wealthy.

Google has resourced its science start-up with some serious intellectual firepower and these scientists and researchers are working behind-the-scenes to challenge the inevitability of death. The proponents of a “transhumanist” movement called the Church of Perpetual Life support Google’s initiative. They believe that technology could one day see our consciousness digitised into computers, turning us from biological humans into robots – the so-called singularity. (Some fear that this will see artificial intelligence morph into a modern-day Frankenstein’s monster!)

For Silicon Valley’s death-cheating initiative to be successful, it must find a way to defy the laws of thermodynamics so that an individual can live forever. The key to immortality is tied to the second law of thermodynamics which states that everything must decay. The cells in our bodies follow that rule and eventually deteriorate. That leads to entropy – the inescapable and irreversible process of disorder and eventual death.

Turnover is a basic characteristic of life. Ergo, the search for the elixir of everlasting life runs against the natural order of things as all living organisms ultimately die. Humans are not biologically immortal and no amount of R&D money can alter that fact. We will all eventually kick the bucket as immortality – the Holy Grail of biological sciences – is a fairy tale. Even if it were possible, I think that a never-ending life would be a fate worse than death.

The death of death has been grossly exaggerated.

Regards

Paul J. Thomas
Chief Executive Officer
Ductus Consulting